Question

A circle with center ‘O’ touches all the four sides of a quadrilateral ABCD internally in such a way that AB is divided in the ratio 3 : 1 and AB = 8 cm, then find the radius of circle if OA = 10 m.

Answer 1

A circle with center O touches the four side of a quadrilateral ABCD of the point E, F, G and H respectively. Contact point E divides side AB in the ratio 3 : 1.

OA = 10 cm

AB = 8 cm

Let AE = 3x

EB = x

∴ AB = AE + EB

⇒ 8 = 3x + x

⇒ 8 = 4x

⇒ x = 2

AE = 3 × 2 = 6 cm

∴ EB = x = 2 cm

From right angled ∆AEO

OA² = AE² + OE²

(10)² = (6)² + (OE)²

(OE)² = (10)² – (6)²

= 100 – 36 = 64

OE = \(\sqrt { 64 }\)

OE = 8 cm

Hence, radius of circle = 8 cm